A240661 Least k such that 6^k == -1 (mod prime(n)), or 0 if no such k exists.

0, 0, 0, 1, 5, 6, 8, 0, 0, 7, 3, 2, 20, 0, 0, 13, 29, 30, 0, 0, 18, 39, 41, 44, 6, 5, 51, 53, 54, 56, 63, 65, 68, 0, 0, 75, 78, 0, 0, 0, 89, 30, 0, 48, 7, 99, 0, 111, 113, 114, 116, 0, 10, 125, 128, 0, 67, 135, 138, 28, 0, 73, 0, 0, 26, 79, 0, 28, 173, 58, 16

Offset: 1

Author

T. D. Noe, Apr 14 2014

Keywords

• nonn

Comments

The least k, if it exists, such that prime(n) divides 6^k + 1.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A211242 (order of 6 mod prime(n)).

Programs

Mathematica

Table[p = Prime[n]; s = Select[Range[p/2], PowerMod[6, #, p] == p - 1 &, 1]; If[s == {}, 0, s[[1]]], {n, 100}]

Formula

a(n) = A211242(n)/2 if A211242(n) is even, otherwise 0.